CAREER: How Diffusion, Dimension, Geometry, and Redundancy Affect Cellular Dynamics

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This project aims to use mathematical modeling to reveal principles underlying (i) how the body defends against foreign invaders such as bacteria and viruses, (ii) how cells cope with stressful environments, and (iii) how cellular processes use random search to find hidden targets with remarkable speed. These diverse problems are united as they all require extending our mathematical understanding of randomness to cope with the complexity of data in modern cell biology. Indeed, a broad goal of this project is to understand how cells function reliably and efficiently despite the ubiquity of randomness at the cellular level. In addition, this project will increase STEM participation and train the next generation of scientists to continue the interdisciplinary approach of this research. In particular, graduate students will be closely involved in all aspects of the work and undergraduates who currently lack access to a research mathematics department will be given a preview of research and graduate school as they participate in summer programs.Cell biology is requiring rapid advances in mathematics, as the data is prompting questions far beyond the limits of existing stochastic processes theory. In the case of T cells interacting with antigens, the PI will develop and apply stochastic models to infer kinetics from raw binary data. In the case of protein-protein interactions, the PI will formulate and analyze a new class of stochastic partial differential equations aimed at uncovering features relating two-dimensional and three-dimensional binding. These models are expected to resolve discrepancies between certain in vivo and in vitro measurements and to show how cells can exploit dimensional-dependent interactions to regulate function. Further, the PI will answer foundational questions in the emerging field of extreme first passage theory. First passage theory has been used extensively to study timescales in biology, but the vast majority of works have focused on the time it takes a given single searcher to find a target. However, the more relevant timescale is often the first passage time of the fastest searcher from a large collection of searchers, as many events in cell biology are initiated by the arrival of the first molecule out of many. The development of extreme first passage theory seeks to discover how redundancy (many copies of proteins, molecules, etc.) affects cellular activation rates and allow a wide range of previous applications of traditional first passage theory to be revised. This project is co-funded by the Cellular Dynamics and Function program in the Division of Molecular and Cellular Biosciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.